Abstract
We present a lattice-QCD determination of the elastic isospin-$1/2$ $S$-wave and $P$-wave $K\pi$ scattering amplitudes as a function of the center-of-mass energy using L\"uscher's method. We perform global fits of $K$-matrix parametrizations to the finite-volume energy spectra for all irreducible representations with total momenta up to $\sqrt{3}\frac{2\pi}{L}$; this includes irreps that mix the $S$- and $P$-waves. Several different parametrizations for the energy dependence of the $K$-matrix are considered. We also determine the positions of the nearest poles in the scattering amplitudes, which correspond to the broad $\kappa$ resonance in the $S$-wave and the narrow $K^*(892)$ resonance in the $P$-wave. Our calculations are performed with $2+1$ dynamical clover fermions for two different pion masses of $317.2(2.2)$ and $175.9(1.8)$ MeV. Our preferred $S$-wave parametrization is based on a conformal map and includes an Adler zero; for the $P$-wave we use a standard pole parametrization including Blatt-Weisskopf barrier factors. The $S$-wave $\kappa$-resonance pole positions are found to be $\left[0.86(12) - 0.309(50)\,i\right]\:{\rm GeV}$ at the heavier pion mass and $\left[0.499(55)- 0.379(66)\,i\right]\:{\rm GeV}$ at the lighter pion mass. The $P$-wave $K^*$-resonance pole positions are found to be $\left[ 0.8951(64) - 0.00250(21)\,i \right]\:{\rm GeV}$ at the heavier pion mass and $\left[0.8718(82) - 0.0130(11)\,i\right]\:{\rm GeV}$ at the lighter pion mass, which corresponds to couplings of $g_{K^* K\pi}=5.02(26)$ and $g_{K^* K\pi}=4.99(22)$, respectively.
Highlights
As the simplest two-meson system with unequal mass and carrying strangeness, the Kπ system plays an important role in particle and nuclear physics
The Kπ system occurs in heavymeson weak decay processes that are used to search for physics beyond the Standard Model [2,3,4,5,6]
On the top-right plot (Λ 1⁄4 A1g, jP⃗ j2 1⁄4 0), there is a downward shift with respect to the noninteracting energies from which we can expect an attractive interaction and a positive S-wave scattering phase shift
Summary
As the simplest two-meson system with unequal mass and carrying strangeness, the Kπ system plays an important role in particle and nuclear physics. The first such calculation, published in 2004, was performed for I 1⁄4 3=2 only and in the quenched approximation [66] This was followed by a calculation in 2006 that included Nf 1⁄4 2 þ 1 staggered sea quarks but employed a domain-wall valence action [67]; the authors determined the I 1⁄4 3=2 S-wave scattering length directly from the lattice and used chiral symmetry to extract the I 1⁄4 1=2 scattering length at several pion masses. The first such studies focused on the P-wave in the KÃ resonance region. [89,90], where the authors calculated the scattering amplitudes in S-, P-, and D-waves with I 1⁄4 1=2 and I 1⁄4 3=2 and determined their resonance content They employed anisotropic gauge ensembles with Nf 1⁄4 2 þ 1 Wilson fermions, to Ref.
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